Optimal. Leaf size=24 \[ 10+\frac {5}{1-x}-\frac {3}{1+e^2-\log (5)} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.38, number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 27, 32} \begin {gather*} \frac {5}{1-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 \int \frac {1}{1-2 x+x^2} \, dx\\ &=5 \int \frac {1}{(-1+x)^2} \, dx\\ &=\frac {5}{1-x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 0.29 \begin {gather*} -\frac {5}{-1+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 7, normalized size = 0.29 \begin {gather*} -\frac {5}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 7, normalized size = 0.29 \begin {gather*} -\frac {5}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 8, normalized size = 0.33
method | result | size |
gosper | \(-\frac {5}{x -1}\) | \(8\) |
default | \(-\frac {5}{x -1}\) | \(8\) |
norman | \(-\frac {5}{x -1}\) | \(8\) |
risch | \(-\frac {5}{x -1}\) | \(8\) |
meijerg | \(\frac {5 x}{1-x}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 7, normalized size = 0.29 \begin {gather*} -\frac {5}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 7, normalized size = 0.29 \begin {gather*} -\frac {5}{x-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.21 \begin {gather*} - \frac {5}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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